Graph (x-7)(x-1)<=0

$(x - 7) (x - 1) \leq 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 7 = 0$

$x - 1 = 0$

Step 2

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Step 3

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 4

The final solution is all the values that make $(x - 7) (x - 1) \leq 0$ true.

$x = 7, 1$

Step 5

Use each root to create test intervals.

$x < 1$

$1 < x < 7$

$x > 7$

Step 6

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

Test a value on the interval $x < 1$ to see if it makes the inequality true.

Choose a value on the interval $x < 1$ and see if this value makes the original inequality true.

$x = 0$

Replace $x$ with $0$ in the original inequality.

$((0) - 7) ((0) - 1) \leq 0$

The left side $7$ is greater than the right side $0$ , which means that the given statement is false.

False

Test a value on the interval $1 < x < 7$ to see if it makes the inequality true.

Choose a value on the interval $1 < x < 7$ and see if this value makes the original inequality true.

$x = 4$

Replace $x$ with $4$ in the original inequality.

$((4) - 7) ((4) - 1) \leq 0$

The left side $- 9$ is less than the right side $0$ , which means that the given statement is always true.

True

Test a value on the interval $x > 7$ to see if it makes the inequality true.

Choose a value on the interval $x > 7$ and see if this value makes the original inequality true.

$x = 10$

Replace $x$ with $10$ in the original inequality.

$((10) - 7) ((10) - 1) \leq 0$

The left side $27$ is greater than the right side $0$ , which means that the given statement is false.

False

Compare the intervals to determine which ones satisfy the original inequality.

$x < 1$ False

$1 < x < 7$ True

$x > 7$ False

$x < 1$ False

$1 < x < 7$ True

$x > 7$ False

Step 7

The solution consists of all of the true intervals.

$1 \leq x \leq 7$

Step 8

Graph (x-7)(x-1)<=0

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